Tagged Questions

There seem to be two primary means of "multiplying" vectors in physics, the cross product and the dot product. Assuming the angle between vectors is defined as $(a)$, the dot product between vectors ...

I am reading an older physics book that my professor gave me. It is going over Coulomb's law and Gauss' theorem. However, the book gives both equations with an $r^3$, not $r^2$, in the denominator. ...

The commutator of generators of Lorentz transformation and translation is as follow:
$$[M^{\mu\nu},P^\sigma]=i(P^\mu\eta^{\nu\sigma}-P^\nu\eta^{\mu\sigma} ).$$
Then from this we usually say that the ...

I know intuitively that the Cross Product of two vectors $\vec{A}$ and $\vec{B}$ represents another vector $\vec{A \times B}$ perpendicular to it. In study of physics we come across this situation a ...

I've been recently introduced to angular displacement, and I'm a little bit confused about it. I think that displacement which is a vector and which is defined as the shortest distance between any two ...

I'm just beginning Shankar's 2nd edition Quantum Mechanics and having some trouble with notation. He defines his vectors as "$\left|V\right>$" . And with a scalar multiplier as "$a\left|V\right>$" . ...

In my textbook, the gravitational field is given by$$\mathbf{g}\left(\mathbf{r}\right)=-G\frac{M}{\left|\mathbf{r}\right|^{2}}e_{r}$$
which is a vector field. On the same page, it is also given as a ...

We have two vectors $F1$ and $F2$ as shown in figure. The change of vectors is shown as $F2-F1$. Why it is it rather than taking negative of vector $F2$ i.e. $-F2$ and then adding it by head-to-tail ...

In a non-orthogonal coordinate system, what is the physically significant difference between the components of a vector on the skew axes and its projection onto each axis? Why would one want to find ...

When a mathematician says something is a scalar, say on the plane, they mean that it associates to points on the plane real numbers. When a physicist says something is a scalar, they mean that if we ...

I was looking for an intuitive definition for dot product and cross product. I have found two similar quesitions in SO, but I am not satisfied with the answers. Finally I found a possible answer here. ...

I have a vector space $V$ and a subspace of $V$, $W$. Let $P$ be the projection operator
for subspace $W$. Also let the dimension of $W$ be $d$. Also I have two orthonormal basis $(a_1,a_2,...a_d)$ ...

If there are a multitude of forces acting on an object in different directions, how do we find the TOTAL force?
I know we add up the $ x $- and $ y $-components of the forces individually, but how do ...

A tensor of type (r,s) on a vector space V is a C-valued function T on V×V×...×V×W×W×...×W (there are r V's and s W's in which W is dual space of V) which is linear in each argument. We take (0, 0) ...

I'm studying the book "Classical Mechanics" by Goldstein together with a coursebook my professor provided.
I'm having trouble grasping how to intuitively determine what the rate of change of a vector ...

Object B is 15 degrees East of North at a distance of 20km/h. Object B is moving at an average speed of 30km/h in the direction 40 degrees East of North. If object A is capable of moving at 100km/h, ...

We can describe fields by two formalisms: vector and spinor. This is the result of possibility of representation of the Lorentz's group irreducible rep as straight cross product of two $SU(2)$ or two ...

If $(\nabla\times\nabla\Phi)_i = \epsilon_{ijk}\partial_j\partial_k\Phi$, where Einstein summation is being used to find the $i$th component...
Using Clairaut's theorem $\partial_{i}\partial_{j}\Phi ...